Taken from The Complete Strategist by John Williams I know a

Taken from \"The Complete Strategist\" by John Williams. \"I know a good game, \" says Alex. \"We point fingers at each other; either one finger or two fingers. If we match with one finger, you buy me one Daiquiri, If we match with two fingers, you buy me two Daiquiris. If we don\'t match I let you off with a payment of a dime. It\'ll help pass the time.\" Olaf appears quite unmoved. \"That sounds like a very dull game at least in its early stages. \" His eyes glaze on the ceiling for a moment and his lips flutter briefly; he returns to the conversation with: \"Now if you care to pay me 42 cents before each game, as a partial compensation for all those 55-cent drinks I\'ll have to buy you, then I\'d be happy to pass the time with you. \" Analyze the above game with and without the side payment. Determine optimal strategies and the value of the game to Olaf. What side payment would make the game air?

Solution

The problem says, the alex will pay for the Dime of 42 cents if they both show two fingers. But if these two show one finger, then Olaf will pay for the Daiquiris which cost 55 cents.

The cost for the two is different. So, optimal solution will be if 3 ,4

If olaf wins 4 times over 3 times by Alex